The TOTEM (TOTal cross section, Elastic scattering and diffraction dissociation Measurement at the LHC) experiment, located at the interaction point 5 of the LHC, has measured the total, elastic and inelastic proton-proton cross-sections, using a luminosity independent method, based on the optical theorem, in a center-of-mass energy range from 2.76 to 13 TeV. The elastic scattering was investigated in a wide range of the squared four-momentum transfer |t| allowing study of the Coulomb-nuclear

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... terference region down to |t| ∼ 8 × 10 −4 GeV 2 . This made possible the first measurement of the ρ parameter at √ s = 13 TeV, ρ being the ratio between the real and the imaginary part of the nuclear elastic scattering amplitude at t = 0. This measurement, combined with the total cross-section results, led to the exclusion of all the models classified and published by the COMPETE Collaboration. The results obtained by TOTEM are indeed compatible with predictions of a colourless 3-gluon bound state exchange in the t-channel of proton-proton elastic scattering, as postulated by alternative theoretical models both in the Regge-like framework and in the modern QCD framework. In this contribution the TOTEM experiment detectors and results will be described, along with the actual experiment status, the future physics program for the LHC Run 3.